Monday, August 06, 2007

Sudoku Lesson I - Develop a Marking System

First, to avoid confusion, let's agree that a "box" is a space where numbers may be recorded and a "square" is a collection of nine boxes, 3 X 3, where the numbers 1-9 are recorded.

As you know, the puzzle comprises nine rows, nine columns and nine squares. The solution has the numbers 1-9 recorded in each row, column and square, with no number repeated. I admit that, when I'm solving a puzzle and I record two numbers the same in any row, column or square, I have borked it. When this happens, I find that it's extremely difficult to determine where I made a mistake. I usually just cross the whole puzzle off and move on. It's ok, you can do the same -- just chalk it up to experience.

The key toward solving any Sudoku puzzle is to have a good marking system. A marking system provides the solver with an indication of possible numbers that can fit in each box. In my system, I place a small dot in the box to indicate that a particular number should go in that box. The location of the dot inside the box determines which number it is.

I place the dot in the box in a 3 x 3 matrix fashion to represent 1-9, starting from top left for 1 and going to bottom right for 9. For example, in one of the boxes, i marked a "3":

For your convenience, I will identify particular boxes by a simple left-to-right, top-to-bottom coordinate system. In this picture, box (1,1) in the first square has a 3 marked in it.

Also in the above picture, box (3,3) has a 2 and a 7 marked in it. I will identify the boxes by column and row. So, for example, the 4 is in box (1, 3).

When recording dots, at first I never place more than two dots in any square, row or column. The reasoning for this will not become apparent to you until much later in the lessons, but if you remember this basic rule, it will make solving the puzzle much easier later on.